Solve (x^2-2x+1)^frac{1{2}}

$$( x ^ { 2 } - 2 x + 1 ) ^ { \frac { 1 } { 2 } }$$

Differentiate w.r.t. x

$$sign(x-1)$$

Steps Using Chain Rule

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$\frac{1}{2}\left(x^{2}-2x^{1}+1\right)^{\frac{1}{2}-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-2x^{1}+1)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\frac{1}{2}\left(x^{2}-2x^{1}+1\right)^{-\frac{1}{2}}\left(2x^{2-1}-2x^{1-1}\right)$$

Simplify.

$$\left(x^{2}-2x^{1}+1\right)^{-\frac{1}{2}}\left(x^{1}-x^{0}\right)$$

For any term t, t^{1}=t.

$$\left(x^{2}-2x+1\right)^{-\frac{1}{2}}\left(x-x^{0}\right)$$

For any term t except 0, t^{0}=1.

$$\left(x^{2}-2x+1\right)^{-\frac{1}{2}}\left(x-1\right)$$

Evaluate

$$|x-1|$$